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Optimality of replication in the CRR model with transaction costs. (English) Zbl 0914.90026
Summary: Recently, there has been a growing interest in optimization problems associated with the arbitrage pricing of derivative securities in imperfect markets (in particular, in models with transaction costs). In this paper, we examine the valuation and hedging of European claims in the multiplicative binomial model proposed by Cox, Ross and Rubinstein (the CRR model), in the presence of proportional transaction costs. We focus on the optimality of replication; in particular, we provide sufficient conditions for the optimality of the replicating strategy in the case of long and short positions in European options. We put emphasis on the martingale approach to the claims valuation in the presence of transaction costs, focusing on call and put options. The problem of optimality of replication in the CRR model under proportional transaction costs was recently solved in all generality by L. Stettner [Appl. Mah. 24, No. 4, 475-514 (1997)].

91B28 Finance etc. (MSC2000)
60G42 Martingales with discrete parameter
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